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The density of states (PDOS) curve and the phonon dispersion curve (PDC) are related to each other, here is how they are related
Density of states (PDOS) curve
We usually use the normalized PDOS, and the graph area enclosed by the PDOS curve and the coordinate axis is 1, so that PDOS can be regarded as a
probability density function .
This probability can be understood as the distribution probability of phonons in the system (from a macroscopic perspective), and can also be understood as the probability of a phonon in a certain state (from the perspective of quantum mechanics).
Phonon dispersion curve (PDC)
The dispersion relationship is actually the relationship function between frequency and wave loss. For a system containing N unique atoms in a unit cell, the dispersion relationship curve has 3N branches, including 3 optical branches and 3(N-1) acoustic branches. .
An important application of the dispersion relation is to obtain the group velocity vg = d ω / d K v_g = d\omega/dKvg=d ω / d K , and the slope of the dispersion curve.
The relationship between PDOS and PDC
The above is the phonon dispersion curve of hexagonal boron nitride. Each point on the curve represents a phonon mode. Count the probability distribution of the above points. Compared with PDOS, it can be seen that the shapes of the two are similar.
In theory, if the system is large enough and there are enough phonon modes, these two curves should coincide.
